Finite Group Databasebeta

← #29590346

Subgroups — #29590346

Order 15616.

456 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449084C211yesmaximal, characteristic
2#21445606C211yesmaximal, characteristic
3#21444138C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic, complemented
5#21443820C211yesmaximal, characteristic, complemented
6#21443818C211yesmaximal, characteristic, complemented
7C61×#1352C211yesmaximal, characteristic, complemented
8C2×#14519737C2211yescharacteristic
9C2×#14519735C411yescharacteristic, complemented
10#16839812—21no—
11C2×#14519691—21no—
12#16839700C411yescharacteristic, complemented
13#16839694C411yescharacteristic, complemented
14#16839688—21no—
15#16839687C2211yescharacteristic
16#16839678—21no—
17C4⋊C4×Dic61—21no—
18C22⋊C4×Dic61—21no—
19C22⋊C4×Dic61—21no—
20#16839609C411yescharacteristic, complemented
21#16839529C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30#14519737—41no—
31#14519737—41no—
32#14519735—41no—
33#14519735—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196C2×C411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—41no—
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47#14519691—24no—
48C22⋊#92418—21no—
49C8×Dic61—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61C2×D411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—41no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C22×Dic61—41no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—42no—
86C2×C8×C61—41no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—42no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—22no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97#11758198—41no—
98#11758198—42no—
99#11758198—42no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102#11758196—41no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—42no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C4×Dic61—82no—
109C2×#92418—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61#13511yescharacteristic
116C23×C61#13511yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C2×C4×C61—22no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C22⋊D61—42no—
136C22⋊D61—42no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61#9911yescharacteristic
154C2×Dic61#9911yescharacteristic
155C2×Dic61#10412yes—
156C4×D61—42no—
157C4×D61—42no—
158C8×C61—81no—
159#92418—81no—
160#11727—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—81no—
170C22×C61C2×#9911yescharacteristic
171C22×C61#41611yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—42no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—82no—
182C4×C61—81no—
183Dic61—21no—
184Dic61—22no—
185Dic61—41no—
186Dic61—81no—
187Dic61—82no—
188Dic61—81no—
189Dic61#35212yes—
190#2395—611no—
191C4×#99—611no—
192#1460—611no—
193#1352—611no—
194#1352D6111yescharacteristic, complemented
195#1344—611no—
196#1344—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—41no—
200C2×C61—41no—
201C2×C61#150111yescharacteristic
202C2×C61C2×#35211yescharacteristic
203C2×C61#212611yescharacteristic
204D61—81no—
205C2×C4×D4—611no—
206C2×#117—611no—
207#431—1221no—
208C2×#99—1221no—
209#400—611no—
210#399C2×D6111yescharacteristic
211#398—611no—
212#397—611no—
213#397—1221no—
214#394—1221no—
215C4×C4⋊C4—1221no—
216C4×C22⋊C4—611no—
217C4×C22⋊C4—1221no—
218C4×C22⋊C4—1221no—
219#342—611no—
220#342C2×D6111yescharacteristic
221#323—611no—
222#323—1221no—
223#323C2×D6111yescharacteristic
224C61#1172711yescharacteristic, complemented, Sylow
225C22×D4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C4×D4—2441no—
229C4×D4—2441no—
230#117—2441no—
231#117—2441no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4C4×D6111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4C22×D6111yescharacteristic
245C2×C42—611no—
246C2×C42—1221no—
247C2×C42—1221no—
248C2×C42—2441no—
249C4⋊C8—2441no—
250#99—1224no—
251C22⋊C8—21no—
252C22⋊C8—1221no—
253C4×C8—2441no—
254#95—611no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259#95—2441no—
260#95C4×D6111yescharacteristic
261C24—611no—
262C24D4×D6111yescharacteristic
263C2×D4—1222no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—2441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—2442no—
280C22×C4—2442no—
281C22×C4—2441no—
282C22×C4C2×C4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C2×C8—41no—
285C2×C8—2441no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C4⋊C4—2442no—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—1222no—
296C22⋊C4—2441no—
297C22⋊C4—2442no—
298C22⋊C4—2442no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C42—1221no—
303C42—1221no—
304C42—4882no—
305C42—2441no—
306C42—2441no—
307C42—2442no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—2441no—
316C23—2441no—
317C23C22⋊C4×D6111yescharacteristic
318C23#1451979811yescharacteristic
319C23#1451980011yescharacteristic
320D4—2442no—
321D4—2442no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—612no—
338C2×C4—1222no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C8—81no—
357C8—4881no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—4881no—
368C22—4881no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22#99×D6111yescharacteristic
373C22#1683975711yescharacteristic
374C22#104×D6111yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—82no—
379C4—81no—
380C4—612no—
381C4—1221no—
382C4—1222no—
383C4—4881no—
384C4—4882no—
385C4—4881no—
386C4—2441no—
387C2—21no—
388C2—21no—
389C2—41no—
390C2—41no—
391C2—4881no—
392C2#2144430911yescharacteristic
393C2#352×D6111yescharacteristic
394C2#2144748111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61#11727
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #21443843C2semidirect
5. #21443820C2semidirect
6. #21443818C2semidirect
7. C61×#1352C2semidirect
9. C2×#14519735C4semidirect
12. #16839700C4semidirect
13. #16839694C4semidirect
20. #16839609C4semidirect
194. #1352D61semidirect
224. C61#11727semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214490842
#214456062
#214441382
#214438432
#214438202
#214438182
C61×#13522
#1172761